Robust Stability of Iterative Learning Control Schemes

A notion of robust stability is developed for iterative learning control in the context of disturbance attenuation. The size of the unmodelled dynamics is captured via a gap distance, which in turn is related to the standard H2 gap metric, and the resulting robustness certificate is qualitatively equivalent to that obtained in classical robust H∞ theory. A bound on the robust stability margin for a specific adaptive ILC design is established

A biased approach to nonlinear robust stability and performance with applications to adaptive control

The nonlinear robust stability theory of Georgiou and Smith [IEEE Trans. Automat. Control, 42 (1997), pp. 1200–1229] is generalized to the case of notions of stability with bias terms. An example from adaptive control illustrates nontrivial robust stability certificates for systems which the previous unbiased theory could not establish a nonzero robust stability margin. This treatment also shows that the bounded-input bounded-output robust stability results for adaptive controllers in French [IEEE Trans. Automat. Control, 53 (2008), pp. 461–478] can be refined to show preservation of biased forms of stability under gap perturbations. In the nonlinear setting, it also is shown that in contrast to linear time invariant systems, the problem of optimizing nominal performance is not equivalent to maximizing the robust stability margin

Evolved embodied phase coordination enables robust quadruped robot locomotion

Overcoming robotics challenges in the real world requires resilient control systems capable of handling a multitude of environments and unforeseen events. Evolutionary optimization using simulations is a promising way to automatically design such control systems, however, if the disparity between simulation and the real world becomes too large, the optimization process may result in dysfunctional real-world behaviors. In this paper, we address this challenge by considering embodied phase coordination in the evolutionary optimization of a quadruped robot controller based on central pattern generators. With this method, leg phases, and indirectly also inter-leg coordination, are influenced by sensor feedback.By comparing two very similar control systems we gain insight into how the sensory feedback approach affects the evolved parameters of the control system, and how the performances differs in simulation, in transferal to the real world, and to different real-world environments. We show that evolution enables the design of a control system with embodied phase coordination which is more complex than previously seen approaches, and that this system is capable of controlling a real-world multi-jointed quadruped robot.The approach reduces the performance discrepancy between simulation and the real world, and displays robustness towards new environments.Comment: 9 page

Interoceptive robustness through environment-mediated morphological development

Typically, AI researchers and roboticists try to realize intelligent behavior in machines by tuning parameters of a predefined structure (body plan and/or neural network architecture) using evolutionary or learning algorithms. Another but not unrelated longstanding property of these systems is their brittleness to slight aberrations, as highlighted by the growing deep learning literature on adversarial examples. Here we show robustness can be achieved by evolving the geometry of soft robots, their control systems, and how their material properties develop in response to one particular interoceptive stimulus (engineering stress) during their lifetimes. By doing so we realized robots that were equally fit but more robust to extreme material defects (such as might occur during fabrication or by damage thereafter) than robots that did not develop during their lifetimes, or developed in response to a different interoceptive stimulus (pressure). This suggests that the interplay between changes in the containing systems of agents (body plan and/or neural architecture) at different temporal scales (evolutionary and developmental) along different modalities (geometry, material properties, synaptic weights) and in response to different signals (interoceptive and external perception) all dictate those agents' abilities to evolve or learn capable and robust strategies

Robustness of the Thirty Meter Telescope Primary Mirror Control System

The primary mirror control system for the Thirty Meter Telescope (TMT) maintains the alignment of the 492 segments in the presence of both quasi-static (gravity and thermal) and dynamic disturbances due to unsteady wind loads. The latter results in a desired control bandwidth of 1Hz at high spatial frequencies. The achievable bandwidth is limited by robustness to (i) uncertain telescope structural dynamics (control-structure interaction) and (ii) small perturbations in the ill-conditioned influence matrix that relates segment edge sensor response to actuator commands. Both of these effects are considered herein using models of TMT. The former is explored through multivariable sensitivity analysis on a reduced-order Zernike-basis representation of the structural dynamics. The interaction matrix ("A-matrix") uncertainty has been analyzed theoretically elsewhere, and is examined here for realistic amplitude perturbations due to segment and sensor installation errors, and gravity and thermal induced segment motion. The primary influence of A-matrix uncertainty is on the control of "focusmode"; this is the least observable mode, measurable only through the edge-sensor (gap-dependent) sensitivity to the dihedral angle between segments. Accurately estimating focus-mode will require updating the A-matrix as a function of the measured gap. A-matrix uncertainty also results in a higher gain-margin requirement for focus-mode, and hence the A-matrix and CSI robustness need to be understood simultaneously. Based on the robustness analysis, the desired 1 Hz bandwidth is achievable in the presence of uncertainty for all except the lowest spatial-frequency response patterns of the primary mirror